## Saving and Capital Formation -- Problems

• Problem 1 -- Corey's wealth
 LIABILITIES ASSETS Bike \$300 Credit card debt \$ 150 Cash \$200 Electric bill \$ 250 Koufax \$ 400 . Checking \$ 1200 . TOTAL = \$ 2100 TOTAL = \$ 400
1. Corey's wealth is \$ 2100 - \$ 400 = \$ 1700.
2. If the Koufax baseball card is found to be a forgery, Corey suffers a capital loss of \$ 400 and his wealth drops to \$ 900.
3. If he uses his income to pay off his credit card balance, his wealth increases by \$ 150. Note that this should count as saving , even though the income was not put into the bank.
4. If he uses his checking account to pay off his liabilities, his assets and his liabilities both drop by the same amount.
5. Of the previous transactions, only using income to pay off the credit card balance counts as saving by the text definition.

• Problem 2 -- Stocks and Flows
Stocks in the sense of this problem refer to the value or quantities of items owned at a given point in time, whenever the items were produced or acquired;
flows refer to changes over a specific period of time.

Assets are stocks; income is a flow.

With this in mind, the classification of the items is easy:

1. GDP is a flow; it is measured quarter by quarter or year by year.
2. National saving is a flow; again, it is measured by the quarter or year.
3. The value of the housing stock is a stock (that one was easy!); we are not looking at the new housing constructed that year, as we would be if we counted residential investment (a flow), but at all the houses in existence now, whenever they were built.
4. The amount of currency in circulation today is a stock; look at the dates on the bills in your wallet; they were not all printed this year.
5. The government budget deficit is a flow; it is part of national saving (or dis-saving) this year .
6. The national debt is a stock; it results from the accumulated total of budget deficits over the course of years, including money borrowed to pay for World War II, Korea and Vietnam.
• Problem 3 -- Motives for Saving

1. Ellie is pregnant and will likely save due to life cycle motives -- to pay for her child's education.
2. Vince reads about layoffs and may save due to precautionary motives.
3. Vince learns he must save if he wants a house; life cycle motives come into play.
4. Ellie wants to go to law school; life cycle saving will be necessary.
5. Capital gains in the stock market may decrease saving if Ellie and Vince have a fixed retirement target; why go to the trouble of saving at all?
6. Saving to leave money to charity is an example of the bequest motive for saving.
• Problem 4 -- Individual Retirement Accounts
The tax advantage of an IRA will motivate Greg to save his \$ 10,000 bonus in an IRA rather than a savings account, even if the expected rate of interest is the same.

The math is simple: you will only have \$ 7,000 to put in the regular savings account after paying taxes, and at the end of 5 years you will have:

Future value = \$ 7000 (1.05) ^ 5

Whereas the IRA will bring:

Future value = \$ 10,000 (1.05) ^ 5

Note though, the impact of the IRA is on deciding how to save; it is not clear that it will have as great an effect on weather to save .

• Problem 5. Saving and Investment
In each of the following, calculate private, public and national savings and the national savings rate.

1. Given that:
1. Household savings = 200
3. Government purchases = 100
4. Government transfers = 100
5. Tax collections = 150
6. Gross Domestic Product = 2,200
We can calculate
1. Govt savings = Tax collections - Transfers - Govt spending, or
Govt savings = 150 - 100 - 100 = - 50

2. Private savings = Household savings + business savings = 600
3. National savings = Govt savings + Private Savings = - 50 + 600 = 550
4. National savings rate = National savings / GDP = 550 / 2200 = 0. 25 or 25 percent

2. Given that:
1. GDP = 6,000
2. Tax collections = 1,200
3. Govt transfers = 400
4. Govt spending = ??
5. Govt budget surplus = 100
6. Consumption expenditures = 4,500
We can calculate
1. Private sector disposable income = GDP - Taxes + Transfers = 6,000 - 1,200 + 400 = 5,200
2. Private sector savings = disposable income - consumption = 5,200 - 4,500 = 700
3. Govt savings = Govt budget surplus = 100
4. National savings = Private savings + Govt savings = 700 + 100 = 800
5. National savings rate = National savings / GDP = 800 / 6,000 = 0.1333 or 13.33 percent
6. Note that since the government budget surplus is given as 100, we can calculate government spending as
100 = Taxes - Transfers - Govt spending

100 = 1,200 - 400 - G

From which it follows that G = 1,200 - 400 - 100 = 700

3. Given that:
1. Consumption = 4,000
2. Investment = 1,000
3. Govt spending = 1,000
4. Net exports = 0
5. Tax collections = 1,500
6. Transfer payments = 500

We can calculate that

1. GDP = C + I + G + NX = 4,000 + 1,000 + 1,000 + 0 = 6,000
2. Govt savings = Taxes - Transfers - Govt spending = 1,500 - 500 - 1,000 = 0
3. Private sector disposable income = GDP - Taxes + Transfers = 6,000 - 1,500 + 500 = 5,000
4. Private sector savings = disposable income - consumption = 5,000 - 4,000 = 1,000
5. National savings = Private savings + Government savings = 1,000 + 0 = 1,000
6. National savings rate = National savings / GDP = 1,000 / 6,000 = 0.1667 or 16.67 percent

4. (Additional problem, showing the relation of government budget deficit and net exports)
Given that:
1. Private sector disposable income = 5,000
2. Consumption = 4,000
3. Investment = 1,000
4. Govt spending = 1,200
5. Net exports = ??
6. Tax collections = 1,500
7. Transfer payments = 500

The numbers are the same as the last problem, except that government spending has increased by 200 .
We can calculate that

1. Govt savings = Taxes - Transfers - Govt spending = 1,500 - 500 - 1,200 = -200
2. Private sector disposable income = GDP - Taxes + Transfers = ??? - 1,500 + 500 = 5,000
3. Private sector savings = disposable income - consumption = 5,000 - 4,000 = 1,000
4. National savings = Private savings + Government savings = 1,000 - 200 = 800
5. National savings = Domestic investment + foreign investment, so
800 = 1,000 + foreign investment , or:
Foreign investment = net exports = - 200
Note the result that an increase of the government budget deficit leads to an increase in the trade deficit.

• Problem 6 -- Data on Saving and Investment The Bureau of Economic analysis has the most recent data on Savings and Investment .

The figures to look at are (figures below are for 2004):

1. Gross private savings = 1,755.3
2. Gross domestic investment = 2300.6
3. Gross government savings = -412.3 + 229.1 = - 183.2
Note that the table gives only Net Government Savings, and we must add the depreciation of fixed capital to get Gross Government Savings.
4. Net borrowing = - 653.4
this is borrowing from the rest of the world due to the Current Account Deficit.
The figures don't quite add up: you must adjust for the statistical discrepancy of 76.8 billion (add to savings, which is most likely to be mismeasured); and for the Capital Account transactions, which add a bit (1.6) to the international accounts.

• Problem 8 -- Movies and the Marginal Product of Capital Given declining marginal returns to the number of screens in a theater complex (not every screen can show the Academy Award winner), the decision of how many screens to build will depend on:
1. the value of the marginal product of capital
2. the rate of interest, which translates into the amount paid per year per screen.
For example, if it costs \$ 1,000,000 to build a screen and the interest rate is 5.5 percent, the annual interest payment will be \$ 55,000 (0.55 times \$ 1,000,000).

Hence given the following table:

Screens Patrons Net revenue VMPK
1 40,000 \$ 80,000 \$ 80,000
2 75,000 \$ 150,000 \$ 70,000
3 105,000 \$ 210,000 \$ 60,000
4 130,000 \$ 260,000 \$ 50,000
5 150,000 \$ 300,000 \$ 40,000

Accordingly,

1. The table requested is given above.
2. If the interest rate is 5.5 percent and the interest payment per screen is \$ 55,000 a year, it will pay to buid 3 screens, but not the fourth -- which would only bring in \$ 50, 000 and would cost \$ 55,000.
3. If the interest rate is 7.5 percent, the interest payment is \$ 75,000 a year, and only the first screen would be profitable.
4. If the interest rate is 10 percent, the interest payment would be \$ 100,000 a year, and even the first screen would not be profitable. No screens will be built.
5. If the interest rate were 5.5 percent, in order to build 5 screens, the total interest payment would have to be no more than \$ 40,000 -- that is,
.055 times COST = \$ 40,000 (where COST is construction costs).

The maximum cost will be \$ 40,000 / 0.055 or \$ 727, 273.

• Problem 9 -- Shifts in the loanable funds market
See graph on page 252 and 253 to fix in mind the picture of the supply curve of savings and the demand for investment.

What happens to the quantity of investment and the interest rate if:

1. Congress passes an investment tax credit ?
By permitting companies to deduct real investment from their taxes, the demand for loanable funds will increase.
The demand curve shifts up and to the right; the interest rate will increase in the new equilibrium.
Although the savings curve does not shift, the quantity of savings will increase -- there will be a movement along the supply of loanable funds curve (= the savings curve).

2. A reduction in military funding moves the government budget into surplus
As a result, the supply of loanable funds increases . The government starts repaying bonds, and so increases the supply of funds flowing into capital markets.
A shift to the left and down of the supply curve in the loanable funds market will decrease the equilibrium interest rate, and will
lead to an increase in the quantity of funds borrowed for investment (a movement along the demand curve for loanable funds.

3. New machinery improves the marginal productivity of capital, and so increases the demand for loanable funds.
The graph should look exactly like that for part a.

4. The tax on corporate profits goes up, so the value marginal productivity of capital (after taxes) decreases.
As a result, the demand for investment shifts to the left and downwards; the equilibrium interest rate falls and the quantity of investment also falls .

5. An increase in precautionary saving will increase the supply of loanable funds, and other things equal, will lead to a lower interest rate and more investment.
(In this case, I would be a bit suspicious of the assumption that other things are equal, since concerns about job security might well mean that the demand for investment has also fallen. But in the terms of the question itself, the shift is in savings).

6. New environmental regulations incrase the cost of operating capital -- and so decrease the value marginal product of capital after those costs are deducted.
As a result, the demand for loanable funds to buy capital decreases , and with the shift of the demand curve downward, interest rates fall and the quantity of loanable funds borrowed decreases . Note that here the interest rate falls and so does the quantity of investment.